Mismatch issues of the crz

[DevelopDaily]

These issues may be related to both qpp #117 and the staq softwareQinc/staq#43, which fixed the state distortion problem by crz and may have introduced some new issues(?)

Here is a test script:

OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];

x q;
crz(1) q[0], q[1];

Qiskit produces the final state:

[ 0+0j, 0+0j, 0+0j, 0.878+0.479j ]

qpp:

0 0 0 0.540302 + 0.841471i

The crz is not documented in https://github.com/softwareQinc/qpp/blob/main/DISCREPANCIES.md.

[525125]

Continuing from #117 (comment):

Since rz and u1 are identical, it only makes sense for crz and cu1 to be identical as well (and they were made the same when fixing crz). This ensures that CRZ = CTRL-diag(RZ).

This is also related to #99

[DevelopDaily]

Mimicking the tests in the issue #117, I did four tests to show the final states out of crz and cu1 on QISKIT and qpp.

In QISKIT:

x q;
crz(pi/3) q[0], q[1];
// => [ 0+0j, 0+0j, 0+0j, 0.866+0.5j ]

x q;
cu1(pi/3) q[0], q[1];
// => [ 0+0j, 0+0j, 0+0j, 0.5+0.866j ]

In qpp:

x q;
crz(pi/3) q[0], q[1];
// => 0  0  0  0.5 + 0.866025i

x q;
cu1(pi/3) q[0], q[1];
// => 0  0  0  0.5 + 0.866025i

The same problem, as expected, exists.

[vsoftco]

@DevelopDaily can you check this now please?

[DevelopDaily]

Passed the simple test cases. Will test more complex cases in the #117